Problem 25 - Chemistry An Atoms First Approach

Question

If you had a mole of U.S. dollar bills and equally distributed the money to all of the people of the world, how rich would every person be? Assume a world population of 7 billion.

Step-by-Step Solution

Answer

If a mole of U.S. dollar bills were equally distributed among the 7 billion people of the world, every person would receive approximately \(8.6 \times 10^{13}\) dollars, which is equivalent to 86 trillion dollars.

Step 1: Find out how many dollar bills are in a mole.

A mole is a unit of measurement used in chemistry to express amounts of a chemical substance. It is equal to Avogadro's constant, which is approximately \(6.022 \times 10^{23}\) entities. Since we have a mole of dollar bills, it means we have approximately \(6.022 \times 10^{23}\) dollar bills.

Step 2: Calculate the money received by each person.

To find out how much money each person would receive, we need to divide the total number of dollar bills by the world population: Money received by each person = \(\frac{Total \, number \, of \, dollar \, bills}{World \, population}\) Substituting the values we have: Money received by each person = \(\frac{6.022 \times 10^{23}}{7 \times 10^9}\)

Step 3: Simplify the expression.

Now we need to simplify the expression by dividing the numerator by the denominator: Money received by each person = \(\frac{6.022 \times 10^{23}}{7 \times 10^9} = \frac{6.022}{7} \times \frac{10^{23}}{10^9}\) Money received by each person = \(\frac{6.022}{7} \times 10^{(23-9)}\) Money received by each person ≈ \(\frac{6.022}{7} \times 10^{14}\) Now, perform the division: Money received by each person ≈ \(0.86 \times 10^{14}\)

Step 4: Write the final answer in scientific notation and standard notation.

The final answer in scientific notation is approximately: Money received by each person ≈ \(8.6 \times 10^{13}\) dollars To convert this to standard notation: Money received by each person ≈ 86,000,000,000,000 dollars So, if a mole of U.S. dollar bills were equally distributed among the world population, each person would receive approximately 86 trillion dollars.